Math help please

Question

Maria read 42 pages of a book on Monday. She reads 2/5 of the book on Tuesday. If she still had 1/4 of the book to read, how many pages were there in the book?

Answer 1

Hello!

This is a fun one.

Let's see, as with all word problems, first we want to find out what we know:

1. 42 pages on Monday
2. 2/5 pages Tuesday
3. 1/4 pages unread

Next, identify what it is we don't know (the answer of course):

Number of pages in book, let's create a variable called "Pages" to represent this.

You could use "X" or "P" or anything else, but I think calling it what it is makes it easy to read.

What did they tell us? Maria still had 1/4 of the book to read. In other words, she had read 3/4 of the book. Make sense?

How would we write that as a simple expression?

3/4 x Pages = 42 + 2/5 x Pages

See what that says? "3/4 of the pages (what she read) are equal to 42 pages (she read on Monday) plus 2/5 of the pages (and yes, we still don't know how many there are) she read on Tuesday".

Now, we simply solve the problem and we'll know how many pages are in the book.

First, get like terms - things with "Pages" in them - on the same side of the equation:

3/4 x Pages - 2/5 x Pages = 42

Now what do we do? Since both of the values on the left are "Pages", we can combine them like this:

(3/4 - 2/5) x Pages = 42

Oooh, we're getting close now!

Let's get rid of 3/4-2/5 by calculating it. How do we subtract fractions with unlike denominators? Yep, find the lowest common denominator. The easy way here to find a common denominator is to multiply them. So 4x5 = 20, so we know 20 is a common denominator.

That makes our equation:

(15/20 - 8/20) x Pages = 42

which simplifies to:

7/20 x pages = 42

Now just get "Pages" alone and we are done.

Multiply both sides by the "inverse" of 7/20 - which is the same as dividing both sides by 7/20, gives:

Pages = 42 x 20/7

= 840/7

= 120

That's it - there are 120 pages in the book.

Hope that helps!